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Mirrors > Home > NFE Home > Th. List > 3exp2 | GIF version |
Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.) |
Ref | Expression |
---|---|
3exp2.1 | ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ) |
Ref | Expression |
---|---|
3exp2 | ⊢ (φ → (ψ → (χ → (θ → τ)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exp2.1 | . . 3 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ) | |
2 | 1 | ex 423 | . 2 ⊢ (φ → ((ψ ∧ χ ∧ θ) → τ)) |
3 | 2 | 3expd 1168 | 1 ⊢ (φ → (ψ → (χ → (θ → τ)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 ∧ w3a 934 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 |
This theorem is referenced by: 3anassrs 1173 ralrimivvva 2707 sfinltfin 4535 |
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